Lay chicken breasts out on a cookie sheet lined with parchment paper. Sprinkle Cajun seasoning over the chicken breasts (just enough to lightly coat). Flip the breasts over and do the same on the other side.
Bake the chicken breasts in the hot oven for 20 to 30 minutes (they should be fork-tender and juices should run clear with no sign of pink). Remove chicken and cool in the refrigerator.
Cook pasta. When done, shock in ice water to stop the cooking. Drain thoroughly.
Core, seed and julienne peppers. Remove ends from onion, peel, cut in half, then julienne. Combine with the cooked pasta.
Cut cooled chicken breasts in half and then slice 1/2-inch thick in the other direction, across the grain. Add to pasta salad.
Combine last ten ingriedients into dressing and pour over salad.